Let the numbers are x and y
The product of the numbers = 294
So,
[tex]x\cdot y=294\rightarrow(1)[/tex]The quotient of the numbers = 6
So,
[tex]\begin{gathered} \frac{x}{y}=6 \\ x=6y \end{gathered}[/tex]Substitute with x = 6y into the first equation:
So,
[tex](6y)\cdot y=294[/tex]Solve for y:
[tex]\begin{gathered} 6y^2=294 \\ y^2=\frac{294}{6}=49 \\ \\ y=\sqrt[]{49}=\pm7 \end{gathered}[/tex]Now, substitute with y to find x
[tex]\begin{gathered} y=7\rightarrow x=6y=6\cdot7=42 \\ \\ y=-7\rightarrow x=6y=6\cdot-7=-42 \end{gathered}[/tex]So, the answer will be:
The numbers are { 42 and 7 } or { -42, -7 }
